Skip to content

CASIO

User´s Guide

Find

Complex Number Calculations (CMPLX)

Use the key to enter the CMPLX Mode when you want to perform basic calculations that include complex numbers.

  • (CMPLX)

You can use either rectangular coordinates (a+bi) or polar coordinates (r∠θ) to input complex numbers.

Complex number calculation results are displayed in accordance with the complex number format setting on the setup menu.


Example: (2 + 6i) ÷ (2i) = 3 - i (Complex number format: a+bi)

  • 26(i) 2(i)
  • Real part = 3
  • (Re⇔Im)
  • Imaginary part = -i

Example: √2∠45 = 1 + i (Angle unit: Deg, Complex number format: a+bi)

  • 2(∠) 45
  • Real part = 1
  • (Re⇔Im)
  • Imaginary part = i

Note

You can use variables A, B, C, and M only in the CMPLX Mode. Variables D, E, F, X, and Y are used by the calculator, which frequently changes their values. You should not use these variables in your expressions.

The indicator "Re⇔lm" is displayed while a complex number calculation is on the display. Press(Re⇔lm) to toggle the display between the real part (a) and imaginary part (b), and the absolute value (r) and argument (θ).

If you are planning to perform input and display of the calculation result in polar coordinate format, specify the angle unit before starting the calculation.

The θ value of the calculation result is displayed in the range of -180°< θ ≦ 180°.

CMPLX Mode Calculation Examples

Example 1: To obtain the conjugate complex number of 2 + 3i (Complex number format: a+bi)

  • (Conjg)23(i)
  • Real part = 2
  • (Re⇔Im)
  • Imaginary part = -3i

Example 2: To obtain the absolute value and argument of 1 + i (Angle unit: Deg)

Absolute Value:

  • (Abs)1(i)
  • 1.414213562

Argument:

  • (arg)1(i)
  • 45.

Using a Command to Specify the Calculation Result Format

Either of two special commands (r∠θ or a+bi) can be input at the end of a calculation to specify the display format of the calculation results. The command overrides the calculator's complex number format setting.

Example: 1 + i = 1.414213562∠45, 1.414213562∠45 = 1 + i (Angle unit: Deg)

  • 1(i)(r∠θ)
  • r = 1.414213562
  • (Re⇔Im)
  • θ = ∠45
  • 2(∠) 45(a+bi)
  • Real part = 1
  • (Re⇔Im)
  • Imaginary part = i
print this page
Top of page